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Quasifree scattering in deuteron break-up by deuterons
Nuclear Physics Al79
(1972) 385-388;
Not to be reproduced by photopnnt
QUASIFREE
SCATTERING
J. P. BURQ,
Q North-Holland Publishing Co., Amsterdam
or microfilm without written permission from the publisher
IN DEUTERON
J.C. CABRILLAT,
M. CHEMARIN,
BREAK-UP BY DEUTERONS B. ILLE and G. NICOLAI
lnstitut de Physique Nuclkaire, Uniuersitd Claude Bernard de Lyon, 43, Bd du 11 Novembre 1918 69-Mlleurbanne, France Received
29 July 1971
Abstract: The quasifree process was studied in the ‘H(d, dn)‘H reaction at 27.5 MeV for three angular conditions. Neutrons and deuterons were detected in coincidence. The charged particle was identified in a AE - E telescope; the neutron energy was measured by a time-of-flight method. The experimental results are interpreted using the modified simple impulse approximation (MSIA). E
NUCLEAR
REACTION
*H(d,dn)‘H; f&=27.5 MeV; measured deduced n-d quasifree scattering.
o(E, E,, E,, O,, 8,);
1. Introduction Quasifree scattering has been extensively studied these last years, but the most numerous results concern the three-nucleon reactions ‘H (p, p n) ‘H and ‘H (p, p p) n, for energies ranging from 5 to 150 MeV [ref. ‘)I. Quasifree scattering in the reaction: d+d-+d+p+n
(1)
has been studied by Briickmann et al. at 51 MeV [ref. 2)] and recently by Valkovic et al. 3, for energies from 7 to 13 MeV. In this reaction the two-body final-state interactions are not so important than in the p+d break-up. The singlet n-p FSI is forbidden from isospin conservation and there are no strong p-d or n-d FSI. So it may be expected that the QF process dominates reaction (1). The analysis of the QFS is generally performed with the use of the simple impulse approximation 5). General agreement with experiment was found at high energy but the discrepaqcy increases with decreasing energy, the requirements of SIA becoming not fulfilled. This disagreement, which concerns the magnitude as well as the shape of the calculated distributions, can be improved by introducing a lower cut-off radius in the deuteron wave function4). The cut-off radius is usually large, energy dependent, and not physically well motivated. 2. Experimental procedure The experimental set up was quite similar to that described in the preceding paper: A foil of deuterated polyethylene of about 6.5 mg/cm2 average thickness was used for the target. A kinematically complete experiment was realized by the detection and the energy measurement of two particles: 385
J. P. BURQ er al.
386
(i) The deuteron by a AE - E telescope (in order to identify the charged particle). (ii) The neutron by a plastic scintillator; its energy was measured by a time-offlight method. Biparametric spectra (neutron time of flight and deuteron energy) were recorded by means of an on-line computer. The absolute values of the cross sections were obtained by the procedure described in the preceding paper, using the d + d elastic scattering for monitoring purposes. Then the biparametric spectra were projected onto the deuteron axis, after background subtraction and neutron-counter efficiency corrections. The projected spectra are shown in fig. 1, where the errors bars include statistical errors, uncertainty on the monitoring and the efficiency of the neutron counter. 3. Data analysis Quasifree scattering peaks have been obtained for as the transferred momentum to the spectator proton the kinematical line. The experimental distributions are compared with after the subtraction of a phase-space background as distributions are obtained from: d30 dEdd!2,dS2,
three angular conditions such gets through a minimum along simple impulse approximation shown in fig. 1. The theoretical
4
5
10
15
20
25 Ed
M&J
-
Fig. la. QFS peaks for three angular conditions. P.S.: phase-space contribution normalized to the data. Full line: SIA calculations normalized to the experimental data, where N=(d3b/dEdd@,dd52,)_J (d3 aId& do, d%k,cor. Dashed line: Caiculations from MSIA, where R is the cut-off radius.
387
QUASIFREE SCATTERING
2
0
~-’ 10
5
15
20 Ed
t&V
-
Fig. 1b. See fig. 1a.
14,7 < E,, ,_,
-.-
&,= -
< 13,5MeV 1,
25O
en= -3507
--
1 20
Fig. lc. See fig. la.
J. P. BURG et al.
388
TABLE 1
The results %
6”
19 22 25
- 50.7” -45” - 36”
(da/d@Z 57 mb/sr 30 mb/sr 20 mb/sr
N
R
0.15 0.19 0.17
9.5 8.9 9.1
where @(kJ is the Fourier transform of the deuteron wave function and (d~/d~)~~ is the on-the-energy-shell n-d elastic scattering cross sedtion in the c.m. system. It was evaluated from existing data 6, at an incident neutron energy of about 13.5 MeV and corresponding c.m. angles. In order to obtain the same magnitude for theoretical and experimental distributions, we have normalized the SIA by a factor of about 0.18. However the calculated distributions are wider than experimental ones. This is the confirmation that SIA, even with this normalization factor, gives only qualitative agreement at low energy, where the wave length of the incident particle cannot be considered as small compared to the deuteron size. A somewhat artificial method to satisfy the QF conditions is to introduce in the deuteron wave function a lower cut-off radius. The data are very well fitted by such a model as shown in fig. 1. The cut-off radius found by a x2 test is sensibly the same for the three spectra. It appears that the QFS cross sections are following the angular distribution of the free elastic n-d cross sections. The results are summarized in table 1. The values found for the phenomenological parameter R are rather higher than the values determined from the p+d experiments 4). This result does not confirm the hypothesis which have been proposed to explain the discrepancy between experiment and SIA by some FSI. It would be interesting to extend measurements for other deuteron energies and also to compare the reactions ‘H (d, dn)‘H and *H (d, d p)‘H. On another hand, a more elaborated approach to the QFS at low energy appears to be necessary, with the use of Fadeev’s equations or the graph method ‘). Work is now in progress along these lines. References 1) I. Slaus, Three-body problem in nuclear and particles physics, Birmingham (North-Holland, Amsterdam, 1969)
2) H. Brtickmann, W. Kluge and L. Schanzler, 2. Phys. 217 (1968) 350 3) V. Valkovic et al., Communication to the Budapest Symp. on the three body-problem and related topics, Hungary, July 8-11, 1971 4) G. Paic, J.C. Young and D.J. Margaziotis, Phys. Lett.32B (1970) 237; V. Valkovic, W. von Witsch, D. Rendic and G.C. Phillipps, Phys. Lett. 33B (1970) 208 5) A. F. Kuckes, R. Wilson and P. F. Cooper, J. Am. Phys. 15 (1961) 193 6) J. D. Seagrave, Three-body problem in nuclear and partictes physics, Birmingham (Noah-HoiIand, Amsterdam, 1969) 7) V.V. Komarov and A.M. Popova, Nucl. Phys. 54 (1965) 278; V.V. Komarov, S.G. Serebrjakov and A.M. Popova, Phys. Lett. 34B (1971) 275
(1972) 385-388;
Not to be reproduced by photopnnt
QUASIFREE
SCATTERING
J. P. BURQ,
Q North-Holland Publishing Co., Amsterdam
or microfilm without written permission from the publisher
IN DEUTERON
J.C. CABRILLAT,
M. CHEMARIN,
BREAK-UP BY DEUTERONS B. ILLE and G. NICOLAI
lnstitut de Physique Nuclkaire, Uniuersitd Claude Bernard de Lyon, 43, Bd du 11 Novembre 1918 69-Mlleurbanne, France Received
29 July 1971
Abstract: The quasifree process was studied in the ‘H(d, dn)‘H reaction at 27.5 MeV for three angular conditions. Neutrons and deuterons were detected in coincidence. The charged particle was identified in a AE - E telescope; the neutron energy was measured by a time-of-flight method. The experimental results are interpreted using the modified simple impulse approximation (MSIA). E
NUCLEAR
REACTION
*H(d,dn)‘H; f&=27.5 MeV; measured deduced n-d quasifree scattering.
o(E, E,, E,, O,, 8,);
1. Introduction Quasifree scattering has been extensively studied these last years, but the most numerous results concern the three-nucleon reactions ‘H (p, p n) ‘H and ‘H (p, p p) n, for energies ranging from 5 to 150 MeV [ref. ‘)I. Quasifree scattering in the reaction: d+d-+d+p+n
(1)
has been studied by Briickmann et al. at 51 MeV [ref. 2)] and recently by Valkovic et al. 3, for energies from 7 to 13 MeV. In this reaction the two-body final-state interactions are not so important than in the p+d break-up. The singlet n-p FSI is forbidden from isospin conservation and there are no strong p-d or n-d FSI. So it may be expected that the QF process dominates reaction (1). The analysis of the QFS is generally performed with the use of the simple impulse approximation 5). General agreement with experiment was found at high energy but the discrepaqcy increases with decreasing energy, the requirements of SIA becoming not fulfilled. This disagreement, which concerns the magnitude as well as the shape of the calculated distributions, can be improved by introducing a lower cut-off radius in the deuteron wave function4). The cut-off radius is usually large, energy dependent, and not physically well motivated. 2. Experimental procedure The experimental set up was quite similar to that described in the preceding paper: A foil of deuterated polyethylene of about 6.5 mg/cm2 average thickness was used for the target. A kinematically complete experiment was realized by the detection and the energy measurement of two particles: 385
J. P. BURQ er al.
386
(i) The deuteron by a AE - E telescope (in order to identify the charged particle). (ii) The neutron by a plastic scintillator; its energy was measured by a time-offlight method. Biparametric spectra (neutron time of flight and deuteron energy) were recorded by means of an on-line computer. The absolute values of the cross sections were obtained by the procedure described in the preceding paper, using the d + d elastic scattering for monitoring purposes. Then the biparametric spectra were projected onto the deuteron axis, after background subtraction and neutron-counter efficiency corrections. The projected spectra are shown in fig. 1, where the errors bars include statistical errors, uncertainty on the monitoring and the efficiency of the neutron counter. 3. Data analysis Quasifree scattering peaks have been obtained for as the transferred momentum to the spectator proton the kinematical line. The experimental distributions are compared with after the subtraction of a phase-space background as distributions are obtained from: d30 dEdd!2,dS2,
three angular conditions such gets through a minimum along simple impulse approximation shown in fig. 1. The theoretical
4
5
10
15
20
25 Ed
M&J
-
Fig. la. QFS peaks for three angular conditions. P.S.: phase-space contribution normalized to the data. Full line: SIA calculations normalized to the experimental data, where N=(d3b/dEdd@,dd52,)_J (d3 aId& do, d%k,cor. Dashed line: Caiculations from MSIA, where R is the cut-off radius.
387
QUASIFREE SCATTERING
2
0
~-’ 10
5
15
20 Ed
t&V
-
Fig. 1b. See fig. 1a.
14,7 < E,, ,_,
-.-
&,= -
< 13,5MeV 1,
25O
en= -3507
--
1 20
Fig. lc. See fig. la.
J. P. BURG et al.
388
TABLE 1
The results %
6”
19 22 25
- 50.7” -45” - 36”
(da/d@Z 57 mb/sr 30 mb/sr 20 mb/sr
N
R
0.15 0.19 0.17
9.5 8.9 9.1
where @(kJ is the Fourier transform of the deuteron wave function and (d~/d~)~~ is the on-the-energy-shell n-d elastic scattering cross sedtion in the c.m. system. It was evaluated from existing data 6, at an incident neutron energy of about 13.5 MeV and corresponding c.m. angles. In order to obtain the same magnitude for theoretical and experimental distributions, we have normalized the SIA by a factor of about 0.18. However the calculated distributions are wider than experimental ones. This is the confirmation that SIA, even with this normalization factor, gives only qualitative agreement at low energy, where the wave length of the incident particle cannot be considered as small compared to the deuteron size. A somewhat artificial method to satisfy the QF conditions is to introduce in the deuteron wave function a lower cut-off radius. The data are very well fitted by such a model as shown in fig. 1. The cut-off radius found by a x2 test is sensibly the same for the three spectra. It appears that the QFS cross sections are following the angular distribution of the free elastic n-d cross sections. The results are summarized in table 1. The values found for the phenomenological parameter R are rather higher than the values determined from the p+d experiments 4). This result does not confirm the hypothesis which have been proposed to explain the discrepancy between experiment and SIA by some FSI. It would be interesting to extend measurements for other deuteron energies and also to compare the reactions ‘H (d, dn)‘H and *H (d, d p)‘H. On another hand, a more elaborated approach to the QFS at low energy appears to be necessary, with the use of Fadeev’s equations or the graph method ‘). Work is now in progress along these lines. References 1) I. Slaus, Three-body problem in nuclear and particles physics, Birmingham (North-Holland, Amsterdam, 1969)
2) H. Brtickmann, W. Kluge and L. Schanzler, 2. Phys. 217 (1968) 350 3) V. Valkovic et al., Communication to the Budapest Symp. on the three body-problem and related topics, Hungary, July 8-11, 1971 4) G. Paic, J.C. Young and D.J. Margaziotis, Phys. Lett.32B (1970) 237; V. Valkovic, W. von Witsch, D. Rendic and G.C. Phillipps, Phys. Lett. 33B (1970) 208 5) A. F. Kuckes, R. Wilson and P. F. Cooper, J. Am. Phys. 15 (1961) 193 6) J. D. Seagrave, Three-body problem in nuclear and partictes physics, Birmingham (Noah-HoiIand, Amsterdam, 1969) 7) V.V. Komarov and A.M. Popova, Nucl. Phys. 54 (1965) 278; V.V. Komarov, S.G. Serebrjakov and A.M. Popova, Phys. Lett. 34B (1971) 275